Why did alexander hamilton encourage federalist to vote for Jefferson instead of Burr?

Answer 1

Hamilton disliked both Burr and Jefferson, but he felt that Jefferson was at least honest. (In fact, such a quote was atributed to him: "At least Jefferson was honest.")

On the other hand, Hamilton (and lots of other people) felt that Burr was a dishonest opportunist, who couldn't be trusted. Hamilton preferred to have an honest enemy than a dishonest one in the presidency.

Answer 2

Because Hamilton and Burr were extremely bitter political rivals. It got so nasty and personal that they engaged in a duel where Hamilton was killed by Burr. A very good book to read about their conflict is "Burr" by Gore Vidal.